This paper proposes a model of the process by which players learn to play repeated coordination games, with the goal of understanding the results of some recent experiments.In those experiments the dynamics of subjects' strategy choices and the resulting patterns of discrimination among equilibria varied systematically with the rule for determining payoffs and the size of the interacting groups, in ways that are not adequately explained by available methods of analysis.The model suggests a possible explanation by showing how the dispersion of subjects' beliefs interacts with the learning process to determine the probability distribution of its dynamics and limiting outcome.

[This paper studies the limits of contracting as a method for achieving efficient allocation, with particular attention to how informational asymmetries interact with the timing of commitment to a mechanism. There are arguments to suggest, in the spirit of the Coase "Theorem," that if agents can agree on a mechanism before observing their private information (or, a fortiori, if information is perfect or symmetric), they can realize an incentive-efficient allocation. If, however, agents observe their private information before contracting, there may be further restrictions, due to information leakage during the process of bargaining over mechanisms, on what they can achieve by contract. These restrictions are characterized and compared to those proposed for this setting by Holmstrom and Myerson [6]. It is also shown that there is at least one specification of the rules that govern mechanism design that makes it possible for agents to achieve, contracting after they observe their private information, the same incentive-efficient allocations that are attainable when they can commit themselves to a mechanism before observing their private information.]

[This paper proposes a simple theory to explain bargaining impasses, which is based on Schelling's view of the bargaining process as a struggle between bargainers to commit themselves to favorable bargaining positions. Because bargaining impasses are generally Pareto-inefficient, anything involving a positive probability of impasse is Pareto-inefficient as well. It is demonstrated that in spite of this avoidable inefficiency, when successful commitment is uncertain and irreversible it can still be rational for individuals to attempt commitment and thereby risk an impasse; in a leading special case, the model reduces to a Prisoner's Dilemma game, in which only strategic-dominance arguments are needed to establish this conclusion. Further, making commitment more difficult, or changing the costs of disagreement in a way that makes available a wider range of settlements that are better for both bargainers than disagreement, need not always lower the probability of impasse, in spite of the conventional wisdom to the contrary.]

[This paper describes a simple, operational procedure that, under reasonable economic assumptions, always generates Pareto-efficient egalitarian-equivalent allocations (PEEEA) when agents know each other's preferences. The procedure constitutes a new, constructive proof of Pazner and Schmeidler's theorems on the existence of PEEEA, and shows that PEEEA, like fair and Pareto-efficient allocations, can be decentralized using less information than is required by the standard market procedure for decentralizing allocations that maximize a neoclassical, individualistic social welfare function.]

[This paper investigates the possibility of arriving at the mixed-strategy solution of a zero-sum two-person game through an iterative learning process. Learning takes place during repeated play of the game, in which the players have no direct knowledge of the payoff matrix but are allowed to record what happens during play. In this context, all members of a wide class of behaviorally plausible learning mechanisms are shown to be locally unstable for "almost all" zero-sum two-person games with mixed-strategy solutions.]

Competitive adjustment processes in labor markets with perfect information but heterogeneous firms and workers are studied. Generalizing results of Shapley and Shubik [7], and of Crawford and Knoer [1], we show that equilibrium in such markets exists and is stable, in spite of workers' discrete choices among jobs, provided that all workers are gross substitutes from each firm's standpoint. We also generalize Gale and Shapley's [3] result that the equilibrium to which the adjustment process converges is biased in favor of agents on the side of the market that makes offers, beyond the class of economies to which it was extended by Crawford and Knoer [1]. Finally, we use our techniques to establish the existence of equilibrium in a wider class of markets, and some sensible comparative statics results about the effects of adding agents to the market are obtained. THE ARROW-DEBREU THEORY of general economic equilibrium has long been recognized as a powerful and elegant tool for the analysis of resource allocation in market economies. Not all markets fit equally well into the Arrow-Debreu framework, however. Consider, for example, the labor market-or the housing market, which provides an equally good example for most of our purposes. Essential features of the labor market are pervasive uncertainty about market opportunities on the part of participants, extensive heterogeneity, in the sense that job satisfaction and productivity generally differ (and are expected to differ) interactively and significantly across workers and jobs, and large set-up costs and returns to specialization that typically limit workers to one job. All of these features can be fitted formally into the Arrow-Debreu framework. State-contingent general equilibrium theory, for example, provides a starting point for studying the effects of uncertainty. But this analysis has been made richer and its explanatory power broadened by the examination of equilibrium with incomplete markets, search theory, and market signaling theory. The purpose of this paper is to attempt some improvements in another dimension: we study the outcome of competitive sorting processes in markets where complete heterogeneity prevails (or may prevail). To do this, we take as given the implications of set-up costs and returns to specialization by assuming that, while firms can hire any number of workers, workers can take at most one job. We also return to the simplification of perfect information. In the customary view of competitive markets, agents take market prices as given and respond noncooperatively to them. In this framework equilibrium cannot exist in general unless the goods traded in each market are truly homogeneous; heterogeneity therefore generally requires a very large number of markets. And since these markets are necessarily extremely thin-in many cases containing only a single agent on each side-the traditional stories supporting the plausibility of price-taking behavior are quite strained.

[Competitive adjustment processes in labor markets where firms and workers are heterogeneous but well informed are studied. A natural notion of equilibrium for such markets is defined, and a plausible adjustment process is shown under reasonable assumptions always to converge to an equilibrium; this allows a generalization of several existence results in the literature. Finally, the relationship between market institutions (such as who makes offers) and which of the range of equilibria that heterogeneity makes possible arises, is studied. Generalizing results of Gale and Shapley and Shapley and Shubik, it is shown that all agents on a given side of the market agree on which is the best equilibrium, and that the equilibrium that emerges is the one most favored by the agents on the side of the market that makes offers in the adjustment process. The process can also be viewed as an algorithm for transportation and optimal assignment problems.]

This paper reports experiments designed to measure strategic sophistication, the extent to which players' behavior reflects attempts to predict others' decisions, taking their incentives into account. Subjects played normal-form games with various patterns of iterated dominance and unique pure-strategy equilibria without dominance, using a computer interface that allowed them to look up hidden payoffs as often as desired, one at a time, while automatically recording their look-ups. Monitoring information search allows tests of game theory's implications for cognition as well as decisions, and subjects' deviations from search patterns suggested by equilibrium analysis help to predict their deviations from equilibrium decisions.

This paper proposes a structural nonequilibrium model of initial responses to incomplete-information games based on “level-k” thinking, which describes behavior in many experiments with complete-information games. We derive the model's implications in first- and second-price auctions with general information structures, compare them to equilibrium and Eyster and Rabin's (2005) “cursed equilibrium,” and evaluate the model's potential to explain nonequilibrium bidding in auction experiments. The level-k model generalizes many insights from equilibrium auction theory. It allows a unified explanation of the winner's curse in common-value auctions and overbidding in those independent-private-value auctions without the uniform value distributions used in most experiments.

This paper proposes a characterization of optimal strategies for playing certain repeated coordination games whose players have identical preferences. Players' optimal coordination strategies reflect their uncertainty about how their partners will respond to multiple-equilibrium problems; this uncertainty constrains the statistical relationships between their strategy choices players can bring about. The authors show that optimality is nevertheless consistent with subgame-perfect equilibrium. Examples are analyzed in which players use precedents as focal points to achieve and maintain coordination, and in which they play dominated strategies with positive probability in early stages in the hope of generating a useful precedent.